Power-measured pulses for thermal trimming

ABSTRACT

A circuit for trimming a thermally-trimmable resistor, measuring a temperature coefficient of resistance of the thermally-trimmable resistor, and annealing a thermally-trimmable resistor post-trimming, the circuit comprising: a thermally-isolated area on a substrate housing the thermally-trimmable resistor; heating circuitry for applying a signal to a heating resistor; and a constant-power module adapted to maintain power dissipated in the heating resistor substantially constant over a duration of the signal by varying at least one parameter of the signal as a result of a change in resistance of the heating resistor during the signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority of U.S. Provisional PatentApplication No. 60/762,884, filed on Jan. 30, 2006.

TECHNICAL FIELD

The invention relates to resistors and resistor networks which areelectro-thermally trimmable, and more specifically, to thermal trimmingof these resistors to adjust parameters such as resistance, temperaturecoefficient of resistance and relative temperature coefficient ofresistance.

BACKGROUND OF THE INVENTION

Prior art on thermal trimming of resistors has disclosed and addressedseveral configurations and variations. Thermal trimming of athermally-mutable resistor is possible whether or not it is residing onor in a thermally-isolated microstructure. Also, there may or may not bea separate auxiliary heater used to apply heating power to a functionalresistor which is intended to be trimmed. A sequence of electric voltageor current pulses is applied to a resistor (whether separate or not), inorder to thermally trim the functional resistor.

For example, in Feldbaumer D W et al: “Pulse current trimming ofpolysilicon resistors”, simple functional resistors made from depositedpolysilicon embedded within surface films in an integrated circuit chipcan be thermally-trimmed by simply passing a high-enough current (orcurrent density) through that resistor to sufficiently raise itstemperature. Others propose a melting-segregation model to explain theself-trimming phenomena. U.S. Pat. No. 5,466,484 teaches the use of anauxiliary heating resistor to heat a functional resistor, where aheating voltage or current is applied to that separate heating resistorin order to raise the temperature of the functional resistor. WO03/023794 discloses thermally-trimmable devices using thermally-isolatedmicrostructures, such as micro-platforms suspended over cavities insilicon, in order to achieve higher temperatures at lower voltages andcurrents.

In general, thermal trimming has been disclosed, done by “self-trimming”where the electric trimming signals are applied directly to thefunctional resistor, or done by applying the trimming signals to aseparate auxiliary heater-resistor. In both cases, there is potentiallya fundamental problem with the stability of the resistor to which thetrimming signals are applied. Hereafter in this text, this resistor willbe referred to as the “heater-resistor”, regardless of whether it is thesame physical resistor as the functional resistor targeted for thermaltrimming. If this heater-resistor is itself thermally-mutable, then thetemperature of the target functional resistor (which may be the sameresistor as the heater-resistor) may change during the trimming signals,from one pulse to the next for a constant-level input signal, or evenduring the course of a single trimming pulse at a constant voltage orcurrent. Such variations in electric resistance in the heater-resistorcan lead to unpredictable changes in dissipated power, and loss ofcontrol over the trimming process. An example of this situation isdepicted in FIG. 1.

Indeed, the heater-resistor typically is thermally-mutable. In the caseof a separate auxiliary heater-resistor, it is often desirable to makethe heater-resistor out of materials typically available in a standardsemiconductor integrated circuit process—it is often not convenient todesign or incorporate into the fabrication process a special materialfor the separate heater-resistor. For example, since the heater-resistormaterial must be compatible with trimming temperatures, in manyprocesses the only practical material is a deposited polycrystallinesilicon (or SiGe) resistor. Metals (e.g. Al, Cu) may melt at thermaltrimming temperatures such as (700-800° C.), and resistors diffused intothe bulk silicon cannot be effectively thermally isolated from thesubstrate well enough in order to trim resistors typically foundsandwiched between surface dielectric layers. In the present state ofthe art, if the heater is manufactured from a non-thermally-trimmablematerial, or from a material which is relatively stable at thetemperatures needed to thermally trim the functional resistor, then thismay introduce extra complexity (expense, difficulty, and/orinfeasibility), in the manufacturing process.

SUMMARY OF THE INVENTION

Thus, it is proposed to use electric power applied to the heater, as ameasure of trimming pulses instead of voltage or current applied to theheater, to keep control over the heater temperature.

In thermal trimming of thermally-isolated resistors, such as thosehoused in thermally-isolated microstructures, the heater-resistor canbecome unstable during the trimming signal. This instability leads to atleast two problems specific to the context of thermal trimming, namelythermal runaway during a given pulse, and an inability to ensure thatthe temperature induced by a subsequent pulse will have a specificrelationship to the previous pulse, such as being higher or lower by aspecific amount. The instability of the resistor is unpredictable. Thus,it is advantageous that the trimming signals be “power-measured”, whichallows the power (and therefore the temperature) to be known throughout(before, during, and after) a sequence of electrical signals applied tothe heater. It is also advantageous in some cases that the trimmingsignals be “power-controlled”, such that they maintain a substantiallyconstant power dissipation during the signal applied to the heater, evenif the heater-resistance is unstable and changing its materialproperties.

In accordance with a first broad aspect of the present invention, thereis provided a method for trimming a thermally-trimmable resistorthermally-isolated on a substrate, the method comprising: applying asignal to a heating resistor to trim the thermally-trimmable resistor;and maintaining power dissipated in the heating resistor substantiallyconstant over a duration of the signal by varying at least one parameterof the signal as a result of a change in resistance of the heatingresistor during the signal.

In accordance with a second broad aspect of the present invention, thereis provided a method for determining a change in temperature coefficientof resistance, due to thermal trimming, of a thermally-trimmableresistor thermally-isolated on a substrate, the method comprising:measuring at least a first resistance value of the thermally-trimmableresistor at a first temperature; applying a first power-measured heatingsignal to a heating resistor to elevate a temperature of thethermally-trimmable resistor to a second temperature higher than thefirst temperature; measuring at least a second resistance value of thethermally-trimmable resistor at the second temperature; trimming thethermally-trimmable resistor by applying at least one trimming signal tothe heating resistor; measuring at least a third resistance value of thethermally-trimmable resistor at a third temperature; applying a secondpower-measured heating signal to the heating resistor post-trimming toelevate a temperature of the thermally-trimmable resistor to a fourthtemperature higher than the third temperature; measuring at least afourth resistance value of the thermally-trimmable resistor at thefourth temperature; and determining the change in temperaturecoefficient of resistance based on the measured first, second, third,and fourth resistance values using known power values of the firstpower-measured signal and the second power measured signal.

It should be understood that the measurements of the first and secondresistance values can be done in any order. For example, one wayincludes taking a measurement of the first resistance value at roomtemperature, heating the resistor to a second temperature, and takingthe measurement of the second resistance value. Another scenario isheating the resistor to the second temperature, taking the measurementof the second resistance value, and allowing the resistor to cool to thefirst temperature to measure the resistor for the first resistancevalue. Also alternatively, the resistor can be heated to two separatetemperatures and the measurements are taken at each heated temperature.This also applies to the measurements of the third and fourth resistancevalues, which can be done in the same ways.

In accordance with a third broad aspect of the present invention, thereis provided a method for annealing a thermally-trimmable resistorthermally-isolated on a substrate, the method comprising: trimming thethermally-trimmable resistor by applying a first power-measured signalto a heating resistor; and applying a second power-measured signalcorresponding to an average annealing temperature to the heatingresistor, wherein the second power-measured signal has a lower powerlevel than the first power-measured signal.

In accordance with a fourth broad aspect of the present invention, thereis provided a circuit for trimming a thermally-trimmable resistor,measuring a temperature coefficient of resistance of thethermally-trimmable resistor, and annealing a thermally-trimmableresistor post-trimming, the circuit comprising: a thermally-isolatedarea on a substrate housing the thermally-trimmable resistor; heatingcircuitry for applying a signal to a heating resistor; and aconstant-power module adapted to maintain power dissipated in theheating resistor substantially constant over a duration of the signal byvarying at least one parameter of the signal as a result of a change inresistance of the heating resistor during the signal.

In this specification, the term “heating resistor” is intended to meanthe resistor to which a heat pulse is applied for trimming purposes,regardless of whether it is the same physical resistor as the functionalresistor targeted for thermal trimming. The term “signal” is intended tomean a single pulse, a sequence of pulses, or an input code that getstransformed into an electrical signal applied to a component. The term“power” is intended to mean either instantaneous power or time-averagedpower. The term “power-measured” should be understood as meaning asignal having a known power level, power being the parameter by whichthe pulse is measured. The term “power-controlled” should be understoodas meaning a signal where the power level of the pulse is controlled byvarying/setting other parameters which affect the power, such as voltageor current.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1 is an oscilloscope snapshot of the resistance of aheater-resistor, for a constant-voltage pulse applied. Thus, one can seethe change in a heater's resistance during and due to a high temperaturepulse of duration 6 ms;

FIG. 2 top is a bar graph illustrating experimental results of trimmingof resistors by constant-power pulses of increasing amplitude;

FIG. 2 bottom is a bar graph showing a trimming range of resistors usinga sequence of constant-power pulses at varying levels of the referencepower;

FIG. 3 a illustrates a first example of output power subject to changes,even during each single pulse, when input voltage is held constantduring each individual pulse, for typical trimming events;

FIG. 3 b illustrates a second example where output power changes with(and is controlled by), input voltage, but the output power ismaintained constant during each individual pulse;

FIG. 4 is a circuit diagram of a feedback loop used as avoltage-to-power converter;

FIG. 5 a is a circuit diagram of a generic passive voltage-to-powerconverter, using a ballast resistor in series with the heater-resistor;

FIG. 5 b is a circuit diagram of a generic passive current-to-powerconverter, using a ballast resistor in parallel with theheater-resistor;

FIG. 6 shows three examples of voltage, resistance, power andtemperature: (left-side) where there is no ΔR during a constant-voltageinput pulse; (middle) where non-zero ΔR causes unwanted ΔP, andtherefore unwanted ΔT; and (right-side) where the input pulse (voltage)is modulated in order to keep the power constant during the pulse, inorder that the temperature remains constant even while the resistance isbeing thermally-trimmed during the pulse; and

FIG. 7 shows a graph relating behaviour of change in resistance dividedby initial resistance (ΔR/R) vs. temperature (T), for typicalthermally-trimmable materials whose resistance trims down at hightemperatures. Note that this behavior does not take account of anynon-zero temperature coefficients of the thermally-trimmable material.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

This invention proposes a method to mitigate the above-described problemof heater-resistor stability. Thermal trimming is fundamentallycontrolled by temperature, and typically there is no reliabletemperature sensor in the trimming zone (because typically theheater-resistor and functional-resistor may be both unstable at trimmingtemperatures, and because design of another explicit temperature sensorwould raise further inconvenience). Therefore, the resistors,microstructure, and system to apply heating pulses, are co-designed,taking account of the temperature-coefficients (magnitude and sign) ofresistance of the heater, heating-pulse-voltage, pulse-current andpulse-power, speed of resistance changes in the heater-resistor duringthermal trimming, relative temperature ranges of thermal trimmability ofthe heater-resistor and functional resistor, as well as thermal inertiaand thermal isolation of the microstructure(s).

Pulses of constant electric power are used for thermal trimming. It isproposed to use electric power applied to the heater-resistor, as ameasure of intended trimming-pulse amplitude (for controlling trimmingtemperature).

In general, the temperature (T) of the microstructure is G*P, where G isthe “thermal isolation” of microstructure in K/mW. The quantity “thermalisolation” of a microstructure describes how high a temperature can bereached in the microstructure, for a given amount of power dissipated inthe microstructure. Thermal isolation is determined predominantly by theoverall geometry and heat-loss mechanisms, and heat-conductiveproperties of the microstructure materials. P is the power (V*I=V²/R)dissipated in the microstructure as a result of the electric signal(e.g. a pulse of voltage, current or power). In a thermal trimmingcontext, the functional resistor and separate heater, if present, aretypically in close thermal contact (at substantially the sametemperature, or close in temperature). In a thermal trimming context,the thermal isolation, G, (of the device in a microstructure or on asubstrate), is typically far more stable than the trimmable resistanceitself. Even if the thermal conductivities are changing in the materialsin the hottest zone of the structure, the thermal conductivities of thematerials outside the hottest zone should change much less, if at all,and it is these locations which primarily determine the thermalisolation between the structure and its surroundings. For example, in athermally-isolated microstructure consisting of a two-armed cantilever,even if the thermal conductivities of the materials in the maincantilever may change (reversibly or irreversibly) due to hightemperatures, still the thermal isolation will be primarily determinedby the thermal conductivities of the materials in the arms of thecantilevers, where they join the main silicon bulk—and these materialsdo not see the same high temperatures. In this case, the time-varyingtemperature in the microstructure can be described as T(t)=V(t)*I(t)*G.Instability in the heater-resistor is represented by instability ineither V(t) or I(t) or both. Maintaining the stability of one of I(t) orV(t) is not enough, if the other remains unstable. However, if theapplied power, V(t)*I(t), could be well-enough controlled, thenT(t)=P(t)*G, and then the time-variation of the temperature would followthe time-variation of the applied power. Thus, if a constant power isdissipated in the heater-resistor, this should maintain a substantiallyconstant temperature within the target functional resistor, even if theresistance of the heater-resistor is changing.

In order to accomplish this constant power dissipation in theheater-resistor, the voltage and current applied to the heater-resistormust be designed and/or modulated to maintain the desired constantpower. The temperature attained in the heater-resistor should becontrolled especially in cases where the heater temperatures needed fortrimming the functional resistor are quite close beneath thetemperatures at which the heater-resistor would be damaged(open-circuited).

This is true whether or not the thermally-trimmable resistor resides ona microstructure with high thermal isolation. In any case, the method ofdelivery of the power-controlled trimming must be designed with therelevant specific particular properties of thermal-isolation,thermal-inertia, and thermal-trimmability in mind.

If the heater-resistor is an auxiliary resistor separate from thefunctional resistor, then the two resistors may be made of the samematerial or different material. The thermal-mutability properties(temperature range of thermal mutability, and speed of change ofresistance due to thermal pulses within that temperature range), of thetwo resistor materials may be the same or different.

Heater-resistor instability and/or thermal runaway can lead to loss ofcontrol over the trimming process, with degraded trimming performance,in various ways.

For example, consider a sequence of pulses whose voltage is beingincreased in order to begin trimming. The initial pulses at low voltagesmay not trim because they do not raise the temperature of themicrostructure high enough. As the pulse voltage is increased, and thusthe applied heating power is increased, eventually the heater-resistor'sresistance may begin to change. In accord with typical thermal trimmingphenomena, as the temperature is increased, eventually theheater-resistor will be trimmed in a decreasing direction (trimmeddown), and for higher temperatures the trim-down will be accelerated. Atsuch a threshold (which may be typically difficult to measure or know apriori), if the pulse voltage is increased by an increment delta-V (ΔV),this can quickly (in a single pulse) trim the heater-resistance downsubstantially. In this case, the current (and therefore power, given aconstant or increasing voltage) can increase dramatically, thus furtherrapidly trimming down the heater-resistance, thus further increasingcurrent and power, and thus the temperature may quickly increase enoughto melt or otherwise catastrophically damage the heater and/ormicrostructure.

Consider the case where the heater-resistor has a positive temperaturecoefficient of resistance (TCR), and receives a constant-current pulse(abbreviated below as “I+TC”). Voltage V=I*R would be applied. As aconsequence, power V*I is dissipated, raising the temperature of theheater-resistor. Due to the positive TCR, the higher temperatureincreases the resistance. If the current is held constant, the voltagemust increase, which would increase the dissipated power, which would inturn further increase the temperature, leading potentially to a thermalrunaway condition.

Further, the resistance vs. temperature behavior of the heater-resistormay be non-linear, with a positive or negative curvature. If, in theabove “I+TC” case, the resistance vs. temperature relationship had asignificant positive curvature, then this would act to further aggravatethe thermal runaway. Typical thermally-trimmable materials such aspolysilicon tend to have positive (slight or more-significant) curvaturein the behavior of resistance vs. temperature, at least until thetemperature approaches trimming temperatures of the material.

If the system reaches a temperature at which the resistor is unstable,further changes may occur. For example, for typical thermally-trimmablepolycrystalline materials such as polysilicon, if the resistance istrimmed downward, the TCR may simultaneously increase. If such atrim-down temperature is reached, then the instability in resistanceand/or TCR may or may not act to further increase the voltage needed tohold a constant current, and therefore may or may not act to furtherincrease the temperature, and may or may not lead to faster thermalrunaway.

For example, in the particular example of “I+TC” described above, if, asthe temperature reaches the trimming temperature of the heater-resistor,the behavior of resistance vs. temperature were to curve downwards, thiswould tend to limit thermal runaway, at least in this high-temperatureregime.

If instead constant-voltage pulses are used with a positive-TCRheater-resistor (abbreviated “V+TC”), the system initially tends tolimit thermal runaway, since increased resistance tends to reduce thecurrent and thus reduce applied power. However, as trimming temperaturesare reached, if the resistance vs. temperature tended to have a downwardcurvature, this would tend to promote thermal runaway.

Consider also the case where the heater-resistor has a negative TCR, andreceives a constant-voltage pulse (“V−TC”). Current I=V/R would flow. Asa consequence, power V*I is dissipated, raising the temperature of theheater-resistor. Due to the negative TCR, the higher temperaturedecreases the resistance. If the voltage is held constant, the currentwould then increase, which would increase the dissipated power, whichwould in turn further increase the temperature, potentially leading tothermal runaway.

In this “V−TC” case, however, if the behavior of resistance vs.temperature of the heater-resistor curves upwards, this will tend tocounteract thermal runaway.

If constant-current pulses are used with a negative TCR heater-resistor(“I−TC”), the system initially tends to limit thermal runaway, sincedecreased resistance tends to reduce the voltage and thus reduce theapplied power. However, as trimming temperatures are reached, if theresistance vs. temperature has upward curvature, this would tend topromote thermal runaway.

The relative temperature ranges of thermal mutability of theheater-resistor and target functional resistor should be considered. Ifthe temperature range of thermal mutability of the heater-resistor isnot at a significantly higher temperature than that of the targetfunctional resistor, then the heater-resistor may be prone toinstability or thermal runaway during trimming. Similarly, at a giventrimming temperature in the temperature range of trimmability of thetarget functional resistor, if the speed of resistance change of theheater-resistor is not much slower than that of the target functionalresistor, then the heater resistor may be prone to instability orthermal runaway during its use in trimming the functional resistor. Ingeneral, thermal runaway of the heater should be avoided at anytemperature intended for use of the heater. If the heater-resistor isprone to thermal runaway at any intended usage temperature, it may beimportant to use power-control instead of voltage-control orcurrent-control.

Power (P) dissipated on the heater-resistor is P=V²/R. If the heaterresistance decreases significantly due to self-trimming during theheating pulse (or after the previous heating pulse), then, for aconstant applied voltage, the dissipated power in that heater furtherincreases, causing further increase of temperature. This thermal runawayphenomenon can cause the heater to be damaged due to excessively hightemperature (become an open circuit). For example, if a heaterresistance begins at ˜1.5K Ω (fresh untrimmed resistor) and varies to˜700-800Ω (after trimming), then the adaptive trimming algorithm whichregulates the next pulse voltage amplitude depending ondecrement/increment of the trimmable resistor (WO2004/097859) may beable to adapt the heating voltage if the heater resistance decreasesslowly. Unfortunately, it cannot protect the heater from thermal runawayif its resistance decreases rapidly during a single pulse. Note that theprobability of the heater being damaged increases with the extent oftrim-down (difference between R_(start) and R_(target)), which requireshigher temperature.

In general, the tendency toward thermal runaway is determined by theoverall direction and magnitude of resistance instability at hightemperature. This is a combination of positive/negative temperaturecoefficient, non-linearity of temperature coefficients, andnon-tempco-based (thermal-trimming-based) resistance changes at hightemperatures. The behaviour of this combination at high temperatures maybe difficult to predict. Therefore empirical measurement of resistancemay be useful in order to select favorable characteristics for theelectrical pulses applied to the heater-resistor. The electrical pulsesmay be characterized in that the parameter by which they are measured isvoltage, or current, or power.

As another example of degradation of trimming performance, if one wantsto prevent the above-described thermal-runaway condition, one mayattempt to limit the applied voltage or limit any increase in appliedvoltage, such that heater-trim-down is limited during a single pulse,and monitor the resistance of the heater in some way (for example, onemay use the trimming of the functional resistor as an indicator ofchanges in the heater). However, in this case the time required fortrimming may increase substantially, since many pulses may be appliedwhile searching for an appropriate trim-down.

FIG. 1 is an oscilloscope snapshot which depicts the “fresh” heater'smaterial resistance change due to high temperature pulse. The lowerpulse (channel 2) is the trigger signal sent to the oscilloscope. Thisdemonstrates how the heater resistance is decreasing (self-trimming)substantially during a heating voltage pulse of approximately 6 ms.

The upper part of FIG. 2 shows experimentally measured results ofconstant-power trimming of 25 resistors at constant-power pulses ofincreasing amplitude (sequences of 250 20 ms pulses at that constantpower). Each of the 25 resistors was exposed to the same constant powerbeginning at a relatively low amplitude. The power amplitude wasincreased until catastrophic damage events (open-circuited heaters) wererecorded. The progression of damage events is recorded in the upper partof the figure. The power amplitude was increased until eventually all ofthe heaters were open-circuited, and this level is represented as 100%in the horizontal axes of the graphs above. This result shows that at apulse power of 73% of the maximum, there are no damage events.

Next, a fresh set of 5 samples was further tested using a sequence of 1020 ms constant-power pulses at 70% of the reference power. This resultshows that, at a pulse power level which does not cause damage events,one can readily trim down by 43% of the as-manufactured resistancevalue.

The method of the present invention also provides accurate temperaturecontrol during post-trim annealing. Annealing of the trimmed resistor(at T lower than applied during trimming down) improves its stability.In practice, this post-trim annealing can be applied by the sameheater-resistor as used for trimming. However, as was mentioned above,resistance of the heater-resistor after trimming may vary substantially,(for example, from ˜1.5KΩ to ˜700Ω). Note that such large variations inheater-resistance may be present, even if there is no severe thermalrunaway condition as described above (even if the trimming wassuccessful). Since one typically does not have a ready measurement ofthis heater-resistor after trimming, generation of a predeterminedannealing temperature is not practical by using constant voltage orcurrent pulses—constant or known electric power is required to beapplied to the heater. For example, if one trims threethermally-trimmable resistors, the first by only a few percent down, thesecond by 15%-down, and the third by 35%-down, after the end of thetrimming processes, the heater-resistors are likely to have widelydifferent resistances, such as ˜1400Ω, ˜1000Ω, and 700Ω, respectively.This is because the three sequences of trimming pulses will have beenquite different. Then, if one wants to apply a predetermined annealingtemperature for a certain amount of time, the situation is differentfrom that during thermal trimming with feedback. In an adaptive sequenceof trimming pulses, one typically has feedback by measuring theresistor, or a related circuit output, between pulses. However, here thegoal is to apply a single annealing temperature, with little-to-noopportunity for feedback. But with such widely varyingheater-resistances, the true applied power (and thus the temperature inthe target functional resistor), can vary by a factor of two ormore—causing widely different post-anneal results. With the technique ofthe present invention, one can apply a single power-measured electricalpulse, or a sequence of power-measured electrical stimuli, eachcorresponding to an annealing temperature in the heater-resistor (or inthe functional resistor, if different), where one doesn't necessarilylet the structure cool after each pulse or stimulus. Of course,depending on the temperature uniformity in the heater-resistor,functional-resistor, or micro-platform, the annealing temperature mayrepresent an “average” or “effective” temperature. The electrical pulsesor stimuli may each correspond to different temperatures.

Instantaneous TCR measurements are also possible using the method of thepresent invention. It is known that poly-silicon may in many caseschange its TCR during thermal trimming. The thermal isolation (G, inK/mW) of microstructures can be found experimentally, and is notexpected to change significantly with trim. Assuming that trimmingdoesn't change this characteristic thermal isolation appreciably, onecan use constant-power pulses to measure the TCR. The temperature ofmicrostructure can be increased by a certain value ΔT (still far belowtrimming temperatures), by applying predetermined power P=ΔT/G whichcauses resistance change ΔR. In this case TCR (in ppm/K) of thepoly-silicon resistor can be calculated as:TCR=ΔR/(RΔT)=(R(T0+ΔT)−R(T0))/(RΔT),

where T0 is operating temperature of poly-silicon resistor.

Reliable control of heater temperature can be achieved by applying awell-determined amount of power instead of voltage. FIG. 3 a shows anexample where the trimming hardware (“Trimming Tool”) applies voltagepulses to the heater. The desired input signals are represented as anumerical “code” (digital input). These input signals are translatedinto analog electrical signals by a Digital-to-Analog converter (DAC),creating a sequence of voltage pulses applied to the heater, Vh vs. t.As described above, if the resistance of the heater changes due tothermal instability, the dissipated power may vary widely during thepulse train, even during an individual pulse, as shown in the lowerplot, Ph vs. t.

FIG. 3 b, on the other hand, shows a voltage-to-power (V-to-P) converterin the signal path, to resolve this problem. The V-to-P convertertransforms input voltage into output power (e.g. delivering an outputpower proportional to input voltage, for example 1V=100 mW),independently from the instantaneous value of the output load (heater)resistance.

The V-to-P converter adjusts the instantaneous output voltage, tocompensate for changes in heater resistance during a single pulse, suchthat the output power remains determined by the input voltage. This isshown by the correspondence in FIG. 3 b between Ph vs. t and the inputcode.

In general, the input code represents the desired level of power thatone wants to be dissipated in the heater-resistor. This input code canreside in many forms, such as in the preferences of a person executing amanual trimming sequence, or in the decisions made by an automatedtrimming algorithm, or in a pre-determined sequence of pulses recordedin any memory medium. In practice, the input code is often “decided” bya computer program, and sent to trimming circuitry as digital signals.In such a case, the digital signals can be converted from digital toanalog signals, typically as voltages or currents, where the analogamplitude of the voltage or current represents the desired power to bedissipated in the heater-resistor. It is also possible that, in thesignal path, the code is converted to a frequency of an oscillatingsignal, or a pulse-width of pulses within a high-frequency pulse-train,or any other parameter of an electrical signal. No matter how the “code”is stored, transmitted or delivered, before it is applied to theheater-resistor it is converted into an amount of dissipated power whichremains substantially constant even while the heater-resistance may bechanging, even during a single pulse applied to it.

Therefore, many specific conversion schemes may be useful at one pointor another in the signal path from “code” to heater-resistor. Withoutlimiting the scope of the invention, several specific cases are outlinedbelow. For example, active voltage-to-power (V-to-P) conversion isdescribed, with the understanding that if the “code” is delivered as acurrent, active current-to-power (I-to-P) conversion is also availableusing typical electrical engineering analysis techniques.

FIG. 4 shows the simplified block diagram for a feedback loop for aV-to-P converter. For simplicity, the feedback loop frequency responseis not discussed here. Basically, the feedback loop time delay was setas a function of the thermal inertia of the heater. The followingequations describe the circuit operation:dV=Ih×Rref  (1)Ph=Vh×Ih  (2)Vinp=Vph, when Gain>>1  (3)where:

-   dV—voltage drop across Rref (V)-   Ih—heater current (A)-   Rref—reference resistor (Ohm)-   Rh—heater (Ohm)-   Ph—heater dissipated power (W)-   Vh—heater voltage (V)-   Vinp—input voltage (V)-   Vph—voltage equivalent of power dissipated in the heater (V)-   Gain—gain of the feedback loop.

The converter consists of three major components—the fixed referenceresistor R_(ref) to create a voltage drop proportional to the currentpassing through an auxiliary heater; the amplifier A2 to amplify theabove-mentioned voltage; and the analog multiplier M1 to produce thevoltage, Vph, equivalent to dissipated power Ph. This type of activeconverter maintains the power Ph=Ih*Vh applied to the heater-resistor,proportional to the voltage input from the digital code.

A passive implementation for V-to-P conversion is shown in FIG. 5. Itcomprises only one component—a fixed-value ballast resistor Rb. In thiscase the heater's current Ih and voltage Vh can be found as:Ih=Vinp/(Rb+Rh)=>decrease of Rh increases Ih  (5)Vh=Vinp/(1+Rb/Rh)=>decrease of Rh decreases Vh  (6).

From equations (5) and (6), it follows that Ih and Vh compensate eachother to a significant extent, improving the consistency of the heater'sdissipated power Ph, as Rh varies.

For example:

-   1. Rb=1 k;-   Initial heater resistance Rh0=1 k; Vinp=2V, then-   Ih0=1 mA, Vh0=1V, Ph0=1 mW.-   If heater resistance Rh due to trimming becomes 0.9 k, then-   Ih=1.052 mA, Vh=0.947V, Ph=0.996 mW.-   dP=(Ph−Ph0)/Ph0×100%=0.4%-   2. Rb=0;-   Initial heater resistance Rh0=1 k; Vinp=1V, then-   Ih0=1 mA, Vh0=1V, Ph=1 mW.-   The same 10% heater resistance change will result:-   Ih=1.111 mA, Vh=1V, Ph=1.111 mW-   dP=(Ph−Ph0)/Ph0×100%=11.1%

Fundamentally, this passive conversion technique relies on therelationship between the resistance values Rh and Rb. Rh must remainrelatively close to Rb when the heater-resistor is at temperaturesrequired for trimming the functional resistor (which may or may not bethe same resistor as the heater-resistor). During trimming, theheater-resistor may vary substantially (e.g. by a percentage as great as50%). The value of Rb should be chosen to keep Rb roughly in the centerof the range of resistances which the heater-resistor may assume duringtrimming of the functional resistor (the range of resistances which theheater-resistor may assume at heater-resistor temperatures such that thefunctional resistor is trimmed). If this conversion scheme is to be usedfor local annealing of the functional resistor at temperaturesrelatively lower than typical thermal trimming temperatures (such thatlittle-to-no resistance change occurs), then the range of resistancesshould include as well the resistance values of Rh in thetemperature-range needed for annealing of the functional resistor. Inorder for the ballast resistor Rb to remain fixed during theheater-resistor's temperature excursions, Rb should be located outsideof the physical space which is heated by the heater-resistor, OR shouldhave very low TCR and have stable Rb in a temperature range whichincludes the temperature at which the heater becomes thermally unstable.Similar to the above passive V-to-P conversion, passive I-to-Pconversion can be readily implemented by connecting a fixed-value Rb inparallel with the heater-resistor, Rh.

In many instances some compromises must be made regarding V-to-Pconverter design. In the case of FIG. 5 a, the tradeoff is betweensimplicity and direct matching of response-time (passive case), vs.accuracy of V-to-P conversion (active case). Note also that in FIG. 5 a,the trimming voltages input to the V-to-P converter must beapproximately double the voltage applied to the heater-resistor. Ifsimplicity and bipolarity are of primary importance, the R ballastdesign may be chosen, at the cost of decreased precision and the needfor approximately two times increased value of input voltage Vinp. Thespeed of response of such a passive power-control scheme will be limitedby the parasitic capacitance and inductance of the resistors Rb and Rh,and associated interconnection conductors, or by the output impedance ofthe voltage- or current-source. These must be designed to be fastenough—faster than the greatest speed of resistance change (ohms pertime or resistance-fraction per time) in the heater resistor duringthermal trimming operations.

In designing passive V-to-P conversion as described above, the ratio ofballast resistance, Rb, to the initial (untrimmed) heater resistance,Rh₀, is considered. This ratio is selected bearing in mind that (a) Rhat trimming temperatures will be different from Rh at room temperature,depending on the temperature coefficients of Rh; and (b) as thermaltrimming of Rh occurs, both its room-temperature resistance and itstemperature coefficients may change as well. Therefore, it may be usefulto experimentally determine the relevant range of resistances which Rhmay assume during intended operation (trimming and potentially annealingand measurement of temperature coefficients, as mentioned above), as abasis for deciding the initial ratio Rb/Rh0. The optimal ratio Rb/Rh0should be decided depending on a tradeoff between desired trim range ofthe heater-resistor, and desired precision within which power must bemaintained by the V-to-P conversion.

Alternatively, if it is desired to provide the input trimming pulses ascurrent-controlled, then it is also possible to use a simple passiveI-to-P conversion circuit, for example that shown in FIG. 5 b. Considerbelow the two cases of Rb=Rh, and Rb=infinite.

-   1. Rb=1 k=Rh-   Rh₀=1 k; I_(inp)=2 mA, then-   Vh₀=1V; Ih₀=1 mA; Wh₀=1 mW.-   Rh→0.9 k-   Ih=1.052 mA, Vh=0.947V; Wh=0.996 mW-   dW=0.4%-   2. Rb=∞-   Rh₀=1 k; I_(inp)=1 mA, then-   Ih₀=1 mA, Vh₀=1V; Wh=1 mW-   Rh→0.9 k-   Ih=1 mA; Vh=0.9V; Wh=0.9 mW-   dW=10%

There are other ways to implement V-to-P or I-to-P conversion. The twoalready described above may be characterized as (1) “active analogmultiplier”, and (2) “passive” (also analog). In addition, there can bepulse-width-modulation. In pulse-width modulation (PWM), a sequence ofpulses are applied, where the duration of the pulses and/or separationbetween pulses is modulated. The pulses may be of constant width withseparations varying, or constant separation with pulse-widths varying,or constant period with duty-cycle (pulse-width) varying. One typicallyuses PWM when the frequency of the pulses is considerably faster thanthe ability of the circuit to respond, such that the circuit “accepts”only a time-averaged current or voltage or power. This time-averagedcurrent, voltage or power accepted by the circuit is controlled bymodulating the pulse-width, separation-width or duty-cycle.

Also, one could implement the I*V multiplication inherent in activeV-to-P or I-to-P, conversion by using a “digital multiplier” whichaccepts the analog signals via ADC and returns the appropriatepower-converted signal by DAC.

Typical thermal trimming is intended to be accomplished during a timeperiod when the temperature in the functional resistor is stabilized.Thus, a global purpose of the technique is to stabilize the temperatureduring the trimming time period, which is typically intended to belonger than the transient thermal response time of the microstructure.However, the thermal response time of the microstructure may not beinsignificant compared to the pulse duration (e.g. as shown in FIG. 1).In general, the response time of the V-to-P converter should be properlydesigned, given the thermal response-time of the heater. If the V-to-Pconverter is too slow, then one reaches trimming temperatures withoutbeing at the desired temperature, leading to unpredictable trims.

Furthermore, since trimming of the heater-resistor may happen during asingle trimming pulse, the V-to-P converter must be able to adjust thevoltage applied to the heater-resistor fast enough in order to maintainthe desired constant power, even while the resistance is changing (beingtrimmed). For example, if significant resistance changes may happen inless than 1 ms, then the V-to-P converter should be able to react fasterthan this (e.g. 0.1 or 0.2 ms). As alluded to above,T(t)=G*P(t)=G*V(t)*I(t)=G*V²(t)/R(t)=G*I²(t)*R(t). If R(t) is changingrapidly with time, in order for the temperature T(t) to be adequatelycontrolled even while those changes are occurring, V(t) and I(t) must bemade to react at least as quickly, by the V-to-P or I-to-P conversion.

In practice, one may by experimental measurements determine (a) thethermal response time of reversible temperature-induced resistancechanges in the microstructure, and (b) the speed of (or time taken by)resistance changes in the heater-resistor at the temperatures (or powerlevels) of interest for (needed for) trimming of the functionalresistor. Once these are known (found experimentally or otherwise), thenone may design the loop time delay of an active V-to-P or I-to-Pconverter to be shorter (faster) than the faster of (a) and (b).

In the passive implementation (using only a fixed-value ballastresistor, as described above), the conversion-time will automatically(passively) track the heater-response-time.

This method is particularly useful when the trimming temperatures of thefunctional resistor are approximately equal to, or greater than, thetrimming temperatures of the heater. If the trimming temperatures of theheater are significantly greater than the trimming temperatures of thefunctional resistor, then one may assume that the heater is stableduring trimming, and one can calibrate the heater's TCR and control itvia voltage pulses. In this case, it is still useful to have V-to-P orI-to-P conversion to avoid possible calibration errors.

FIG. 6 develops three examples of relationships between voltage,resistance, power and temperature, during a thermal trimming pulse, inthe case where the resistance has a significant positive TCR. On theleft side of the figure, a constant-voltage pulse is input. Theresistance (inferred from the measured current), rises from itsbefore-pulse room-temperature resistance to its heated value, during thethermal-response time (τ₀) of the microstructure. The power (V²/R) alsoresponds accordingly, reaching its steady-state value after athermal-response transient. Similarly the temperature reaches theintended trimming temperature T_(trim)=G*P. Since there is no change inresistance ΔR during the pulse (other than the thermal responsetransient which manifests due to the natural positive TCR of theresistance material), after the initial transient the temperaturemaintains at constant level until the end of the pulse. At the end ofthe pulse, the temperature returns to room temperature, and, if thermaltrimming occurs during this temperature-drop, then the after-pulseresistance is changed from the before-pulse resistance.

In the middle column of graphs in FIG. 6, the problem motivating thisinvention is shown. Here the resistance changes, even after the initialthermal response transient is finished. It is depicted as ΔR changing inthe negative direction, which causes unwanted instantaneous ΔP, andtherefore unwanted ΔT, during the single pulse. Note that thetemperature has risen near to a “dangerous temperature” at which theheater-resistor is prone to catastrophic damage (open-circuit).

At the right side of FIG. 6, the solution proposed by this invention isdepicted. Instead of maintaining the voltage constant during the pulse,the input voltage is modulated in order to keep the power constantduring the pulse, in order to maintain the temperature constant at T=G*P(after the thermal-response transient, τ₁), even while the resistance isbeing thermally-trimmed (large ΔR) during the pulse.

The power-measured trimming technique, (where the electrical pulse ischaracterized in that the parameter by which it is measured isdissipated power), with the condition that the dissipated power ismaintained substantially constant over the duration of a single pulse,even if there are changes in the resistance in which the power isdissipated, is also applicable to the case where there are severalthermally-isolated micro-platforms, each with a heater-resistor. Thecase where all of the heater-resistors have nominally-equal initialresistance is particularly interesting. These several heater-resistorsmay be connected in parallel or in series, and the present techniqueoffers certain advantages, as compared with using voltage-measuredelectrical pulses.

For example consider the case where five heater-resistors, each havinginitial resistance 5R, are connected in parallel such that the overallresistance is R, and the electrical pulse is voltage-measured, withvalue V_(pulse), and initial pulse power V_(pulse) ²/R. In this case, ifthe resistance of one of the heater-resistors changes with respect tothe others, the electrical pulse voltage should remain constant and this“weak” heater-resistor may be subject to thermal runaway as describedabove. For example if the resistance of the “weak” heater-resistorchanges from 5R to 4R, the current will increase from V_(pulse)/5R toV_(pulse)/4R, thus increasing the power dissipated in that “weak”heater-resistor from V_(pulse) ²/5R to V_(pulse) ²/4R (a factor of 5/4),leading to a significant temperature increase and possibly thermalrunaway.

For comparison, consider the case where the five parallelheater-resistors each have initial resistance 5R, but the electricalpulse is power-measured, with value P_(pulse)=V_(i-pulse) ²/R, whereV_(i-pulse) is the initial pulse voltage. If the resistance of one ofthe heater-resistors changes (decreases) with respect to the others, theelectrical pulse power should remain constant. Since the overallresistance has decreased, in order to maintain constant power thecurrent must increase and the voltage must decrease. For example, if theresistance of the “weak” heater-resistor changes from 5R to 4R, theoverall resistance of the parallel combination decreases from R to(4R∥5R/4)=20R/21, slightly less than R. In order to maintain theconstant power P_(pulse), the voltage must decrease slightly fromV_(i-pulse) to V_(i-pulse)(20/21)^(0.5), and corresponding overallcurrent increasing from V_(i-pulse)/R to V_(i-pulse)/R(20/21)^(0.5). Ofcourse, the power dissipated in the “weak” heater-resistor will increasefrom Vi_(-pulse) ²/5R to Vi_(-pulse) ²(20/21)/4R=Vi_(-pulse) ²(5/21R),which is a factor of 25/21, less than 5/4, with correspondingly lesstendency for thermal runaway.

On the other hand, if the heater-resistors are connected in series,similar analysis (based on Ohm's Law) shows that if a voltage-measuredpulse is used, and if the resistance decreases, the power dissipated inthe “weak” heater-resistor will decrease, naturally compensating for theresistance change and avoiding thermal runaway. If a power-measuredpulse is used, and if the resistance decreases, the power dissipated inthe “weak” heater-resistor will again decrease, but not by as much as ifthe pulse was voltage-measured. However, this natural decrease in powerwill still act to compensate for the resistance change, and avoidthermal runaway.

Similar Ohm's Law analyses can be done for the cases where theresistance instability is in the positive direction (where theresistance increases during trimming). The choice of voltage- orcurrent- or power-measured pulses should be done keeping in mind thedirections and magnitudes of the various types of resistance changes andinstabilities (+/−TC, nonlinearity of temperature coefficients,non-tempco-based resistance changes at high temperatures, and theoverall combination of these effects at high temperatures).

Furthermore, consider FIG. 7. At temperatures near room temperature, notrimming occurs. As temperature increases, a thermal trimming threshold,T_(th), is reached, above which trimming occurs. Whether or not theresistance increases or decreases at temperatures close to and abovethis threshold, it typically decreases at higher temperatures, as theresistance trims down. Thus the curve of ΔR/R (change in resistancedivided by initial resistance) vs T is shown to be negative-sloping inthe high-T portion of the T axis. As the trimming temperature increases,the amount of trim-down increases, represented by this curve becomingmore negative at higher temperatures. However, it is empirically foundthat in some cases of thermally-trimmable materials, such aspolycrystalline silicon, as the temperature increases further, the slopeof ΔR/R becomes less negative.

In the context of thermal trimming of several heater-resistors connectedin parallel using power-measured electrical pulses, and maintaining thepower constant during the pulse even if the resistance changes, thistype of characteristic curve acts in our favor. If one of the parallelheater-resistors does become “weak”, if such an upward curvature occursbefore catastrophic failure, this acts to allow the other resistors(other than the “weak” heater-resistor) to “catch up” (in other words,to be trimmed down faster such that the difference is reduced betweenthe “weak” heater-resistor and the other resistors).

The embodiment(s) of the invention described above is(are) intended tobe exemplary only. The scope of the invention is therefore intended tobe limited solely by the scope of the appended claims.

1. A method for trimming a thermally-trimmable resistorthermally-isolated on a substrate, the method comprising: applying asignal to a heating resistor to trim said thermally-trimmable resistor;and maintaining power dissipated in said heating resistor substantiallyconstant over a duration of said signal by varying at least oneparameter of said signal as a result of a change in resistance of saidheating resistor during said signal.
 2. A method as claimed in claim 1,wherein said signal is a single electrical pulse, and said powerdissipated in said heating resistor is maintained substantially constantover a duration of said single pulse.
 3. A method as claimed in claim 1,wherein said signal is a sequence of pulses, said maintaining powerdissipated in said heating resistor substantially constant comprisesmaintaining a time-averaged power of said signal substantially constantover said sequence of pulses.
 4. A method as claimed in claim 2, whereinsaid maintaining power dissipated in said heating resistor substantiallyconstant comprises maintaining an instantaneous power of said singlepulse substantially constant.
 5. A method as claimed in claim 2, whereinsaid maintaining power dissipated in said heating resistor substantiallyconstant comprises maintaining a time-averaged power of said singlepulse substantially constant.
 6. A method as claimed in claim 1, whereinsaid maintaining power dissipated in said heating resistor substantiallyconstant comprises converting said signal from voltage to power bytransforming input voltage into output power.
 7. A method as claimed inclaim 1, wherein said maintaining power dissipated in said heatingresistor substantially constant comprises converting said signal fromcurrent to power by transforming input current into output power.
 8. Amethod as claimed in claim 1, wherein said maintaining power dissipatedin said heating resistor substantially constant comprises using afeedback loop to compensate for said change in resistance.
 9. A methodas claimed in claim 8, wherein said feedback loop is designed to have aloop delay time shorter than a thermal response time of reversibletemperature-induced resistance changes in a microstructure and shorterthan a speed of resistance change in said heating resistor attemperatures needed for said trimming.
 10. A method as claimed in claim1, wherein said maintaining power dissipated in said heating resistorsubstantially constant comprises providing a ballast resistor in serieswith said heating resistor to increase current and decrease voltageacross said heating resistor as a result of a decrease in resistance ofsaid heating resistor.
 11. A method as claimed in claim 10, wherein saidproviding a ballast resistor comprises selecting a ratio for saidballast resistor versus said heating resistor as a function of a desiredtrim range of said heating resistor and a desired precision for saidmaintaining power dissipated in said heating resistor substantiallyconstant.
 12. A method as claimed in claim 10, wherein said providing aballast resistor comprises selecting a value for said ballast resistorwithin a range of resistances which said heating resistor may assumeduring said trimming.
 13. A method as claimed in claim 1, wherein saidmaintaining power dissipated in said heating resistor substantiallyconstant comprises monitoring a current across said heating resistor andvarying a voltage as a result of a change in said current.
 14. A methodas claimed in claim 1, wherein said maintaining power dissipated in saidheating resistor substantially constant comprises monitoring a voltageacross said heating resistor and adjusting a current as a result of achange in said voltage.
 15. A method as claimed in claim 1, wherein saidapplying a signal to a heating resistor comprises applying said signaldirectly to said thermally-trimmable resistor, which acts as saidheating resistor by self-heating.
 16. A method as claimed in claim 1,wherein said applying a signal comprises choosing parameters of saidsignal as a function of a direction and magnitude of resistanceinstability.
 17. A method as claimed in claim 1, wherein said varying atleast one parameter of said signal comprises pulse-width modulation tochange an average power dissipated during said signal.
 18. A method asclaimed in claim 1, wherein said change in resistance is a change invariation of resistance versus temperature due to material instability.19. A method as claimed in claim 1, wherein said applying a signal to aheating resistor comprises applying a power-measured signal.
 20. Acircuit for trimming a thermally-trimmable resistor, measuring atemperature coefficient of resistance of said thermally-trimmableresistor, and annealing a thermally-trimmable resistor post-trimming,the circuit comprising: a thermally-isolated area on a substrate housingsaid thermally-trimmable resistor; heating circuitry for applying asignal to a heating resistor; and a constant-power module adapted tomaintain power dissipated in said heating resistor substantiallyconstant over a duration of said signal by varying at least oneparameter of said signal as a result of a change in resistance of saidheating resistor during said signal.
 21. A circuit as claimed in claim20, wherein said heating circuitry is adapted to apply at least oneelectrical pulse, and said constant-power module maintains powerdissipated in said heating resistor substantially constant over aduration of a single pulse.
 22. A circuit as claimed in claim 20,wherein said heating circuitry is adapted to apply a sequence of pulses,and said constant-power module maintains a time-averaged power of saidsignal said substantially constant over a duration of said sequence ofpulses.
 23. A circuit as claimed in claim 21, wherein saidconstant-power module is adapted to maintain an instantaneous power ofsaid single pulse substantially constant.
 24. A circuit as claimed inclaim 21, wherein said constant-power module is adapted to maintain atime-averaged power of said single pulse substantially constant.
 25. Acircuit as claimed in claim 20, wherein said constant-power moduleconverts said signal from voltage to power by transforming input voltageinto output power.
 26. A circuit as claimed in claim 20, wherein saidconstant-power module converts said signal from current to power bytransforming input current into output power.
 27. A circuit as claimedin claim 20, wherein said constant-power module comprises a feedbackloop to compensate for said change in resistance.
 28. A circuit asclaimed in claim 27, wherein said feedback loop has a loop delay timeshorter than a thermal response time of reversible temperature-inducedresistance changes in a microstructure and shorter than a speed ofresistance change in said heating resistor at temperatures needed forsaid trimming.
 29. A circuit as claimed in claim 20, wherein saidconstant-power module comprises a ballast resistor in series with saidheating resistor to increase current and decrease voltage across saidheating resistor as a result of a decrease in resistance of said heatingresistor.
 30. A circuit as claimed in claim 29, wherein said ballastresistor has a resistance value within a range of resistances which saidheating resistor may assume during said trimming.
 31. A circuit asclaimed in claim 20, wherein said constant-power module monitors acurrent across said heating resistor and varies a voltage as a result ofa change in said current.
 32. A circuit as claimed in claim 20, whereinsaid constant-power module monitors a voltage across said heatingresistor and adjusts a current as a result of a change in said voltage.33. A circuit as claimed in claim 20, wherein said constant-power modulemodulates a pulse-width of said signal to change an average powerdissipated during said signal.
 34. A circuit as claimed in claim 20,wherein said heating resistor acts as said thermally-trimmable resistorby self-heating.